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Quasi-2D Coulomb systems are of fundamental importance and have attracted much attention in many areas nowadays. Their reduced symmetry gives rise to interesting collective behaviors, but also brings great challenges for particle-based…
In this paper, we study the complexity factor for a charged anisotropic self-gravitating object. We formulate the Einstein-Maxwell field equations, Tolman-Opphenheimer-Volkoff equation, and the mass function. We form the structure scalars…
We present a novel numerical method for solving the elliptic partial differential equation problem for the electrostatic potential with piecewise constant conductivity. We employ an integral equation approach for which we derive a system of…
We show how to adapt the quasi-Newton method to the electronic-structure calculations using systematic basis sets. Our implementation requires less iterations than the conjugate gradient method, while the computational cost per iteration is…
We combine the recently developed many-body Green's function theory for electrons and nuclei with the exact factorization of the wave function. The existing Born-Oppenheimer Green's functions are shown to be special cases of our exact…
We present a method to perform fully selfconsistent density-functional calculations, which scales linearly with the system size and which is well suited for very large systems. It uses strictly localized pseudoatomic orbitals as basis…
Evaluating the total energy of an extended distribution of point charges, which interact through the Coulomb potential, is central to the study of condensed matter. With near ubiquity, the summation required is carried out using Ewald's…
Computational modeling is an integral part of catalysis research. With it, new methodologies are being developed and implemented to improve the accuracy of simulations while reducing the computational cost. In particular, specific…
Density functional theory is generalized to incorporate electron-phonon coupling. A Kohn-Sham equation yielding the electronic density $n_U(\mathbf{r})$, a conditional probability density depending parametrically on the phonon normal mode…
Methods for calculating an electron density of a periodic crystal constructed using non-orthogonal localised orbitals are discussed. We demonstrate that an existing method based on the matrix expansion of the inverse of the overlap matrix…
An algorithm for fast calculation of the Coulombic forces and energies of point particles with free boundary conditions is proposed. Its calculation time scales as N log N for N particles. This novel method has lower crossover point with…
Quantum embedding schemes have the potential to significantly reduce the computational cost of first principles calculations, whilst maintaining accuracy, particularly for calculations of electronic excitations in complex systems. In this…
Recent trends of ab initio studies and progress in methodologies for electronic structure calculations of strongly correlated electron systems are discussed. The interest for developing efficient methods is motivated by recent discoveries…
We resume the recent successes of the grid-based tensor numerical methods and discuss their prospects in real-space electronic structure calculations. These methods, based on the low-rank representation of the multidimensional functions and…
In calculating integral or discrete transforms, use has been made of fast algorithms for multiplying vectors by matrices whose elements are specified as values of special (Chebyshev, Legendre, Laguerre, etc.) functions. The currently…
The evaluation of the electrostatic potential is fundamental to the study of condensed phase systems. We discuss the calculation of the relevant lattice summations by Ewald-type techniques. A model charge density is introduced, that cancels…
We present an efficient computational approach to perform real-space electronic structure calculations using an adaptive higher-order finite-element discretization of Kohn-Sham density-functional theory (DFT). To this end, we develop an…
A direct orbital optimization method is presented for density functional calculations of excited electronic states using either a real space grid or a plane wave basis set. The method is variational, provides atomic forces in the excited…
The dielectric response and structural properties of finite-temperature electron liquids are central to accurately describing the physical behavior of electronic systems. This study presents a robust analytical model for the static…
We develop a linked cluster method to calculate the spectral weights of many-particle excitations at zero temperature. The dynamical structure factor is expressed as a sum of exclusive structure factors, each representing contributions from…